What is -1+(5/6-2)\div (2-1/4) ?

The solution to -1+(5/6-2)\div (2-1/4) is -5/3

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Popular >

-1+(5/6-2)\div (2-1/4)

Solution

- 1 + (\frac{5}{6} - 2) \div (2 - \frac{1}{4})

Solution

- \frac{5}{3}

Solution steps

- 1 + (\frac{5}{6} - 2) \div (2 - \frac{1}{4})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{5}{6} - 2) : - \frac{7}{6}

\frac{5}{6} - 2

\frac{5}{6} - 2 = - \frac{7}{6}

\frac{5}{6} - 2

Convert element to fraction:

2 = \frac{2 \cdot 6}{6}

= - \frac{2 \cdot 6}{6} + \frac{5}{6}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- 2 \cdot 6 + 5}{6}

- 2 \cdot 6 + 5 = - 7

- 2 \cdot 6 + 5

Multiply the numbers:

2 \cdot 6 = 12

= - 12 + 5

Add/Subtract the numbers:

- 12 + 5 = - 7

= - 7

= \frac{- 7}{6}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{7}{6}

= - \frac{7}{6}

= - 1 - \frac{7}{6} \div (2 - \frac{1}{4})

Calculate within parentheses

(2 - \frac{1}{4}) : \frac{7}{4}

2 - \frac{1}{4}

2 - \frac{1}{4} = \frac{7}{4}

2 - \frac{1}{4}

Convert element to fraction:

2 = \frac{2 \cdot 4}{4}

= \frac{2 \cdot 4}{4} - \frac{1}{4}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{2 \cdot 4 - 1}{4}

2 \cdot 4 - 1 = 7

2 \cdot 4 - 1

Multiply the numbers:

2 \cdot 4 = 8

= 8 - 1

Subtract the numbers:

8 - 1 = 7

= 7

= \frac{7}{4}

= \frac{7}{4}

= - 1 - \frac{7}{6} \div (2 - \frac{1}{4})

Multiply and divide (left to right)

\frac{7}{6} \div (2 - \frac{1}{4}) : \frac{\frac{7}{6}}{( 2 - \frac{1}{4} )}

\frac{7}{6} \div (2 - \frac{1}{4})

\frac{7}{6} \div (2 - \frac{1}{4}) = \frac{\frac{7}{6}}{( 2 - \frac{1}{4} )}

= \frac{\frac{7}{6}}{( 2 - \frac{1}{4} )}

= - 1 - \frac{\frac{7}{6}}{( 2 - \frac{1}{4} )}

Add and subtract (left to right)

- 1 - \frac{\frac{7}{6}}{( 2 - \frac{1}{4} )} : - \frac{5}{3}

- 1 - \frac{\frac{7}{6}}{( 2 - \frac{1}{4} )}

- 1 - \frac{\frac{7}{6}}{( 2 - \frac{1}{4} )} = - \frac{5}{3}

- 1 - \frac{\frac{7}{6}}{2 - \frac{1}{4}}

\frac{\frac{7}{6}}{2 - \frac{1}{4}} = \frac{7}{6 \cdot \frac{7}{4}}

\frac{\frac{7}{6}}{2 - \frac{1}{4}}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{7}{6 ( 2 - \frac{1}{4} )}

Join

2 - \frac{1}{4} : \frac{7}{4}

2 - \frac{1}{4}

Convert element to fraction:

2 = \frac{2 \cdot 4}{4}

= \frac{2 \cdot 4}{4} - \frac{1}{4}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{2 \cdot 4 - 1}{4}

2 \cdot 4 - 1 = 7

2 \cdot 4 - 1

Multiply the numbers:

2 \cdot 4 = 8

= 8 - 1

Subtract the numbers:

8 - 1 = 7

= 7

= \frac{7}{4}

= \frac{7}{6 \cdot \frac{7}{4}}

= - 1 - \frac{7}{6 \cdot \frac{7}{4}}

\frac{7}{6 \cdot \frac{7}{4}} = \frac{2}{3}

\frac{7}{6 \cdot \frac{7}{4}}

Multiply

6 \cdot \frac{7}{4} : \frac{21}{2}

6 \cdot \frac{7}{4}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{7 \cdot 6}{4}

Multiply the numbers:

7 \cdot 6 = 42

= \frac{42}{4}

Cancel the common factor:

2

= \frac{21}{2}

= \frac{7}{\frac{21}{2}}

Apply the fraction rule:

\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b}

= \frac{7 \cdot 2}{21}

Multiply the numbers:

7 \cdot 2 = 14

= \frac{14}{21}

Cancel the common factor:

7

= \frac{2}{3}

= - 1 - \frac{2}{3}

Convert element to fraction:

1 = \frac{1 \cdot 3}{3}

= - \frac{1 \cdot 3}{3} - \frac{2}{3}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- 1 \cdot 3 - 2}{3}

- 1 \cdot 3 - 2 = - 5

- 1 \cdot 3 - 2

Multiply the numbers:

1 \cdot 3 = 3

= - 3 - 2

Subtract the numbers:

- 3 - 2 = - 5

= - 5

= \frac{- 5}{3}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{5}{3}

= - \frac{5}{3}

= - \frac{5}{3}

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2(5)(-3)^2

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2/3*1+12

\frac{2}{3} \cdot 1 + 12

Frequently Asked Questions (FAQ)

What is -1+(5/6-2)\div (2-1/4) ?
The solution to -1+(5/6-2)\div (2-1/4) is -5/3